Deck 9: Statistical Inference: Hypothesis Testing for Single Populations

Question 1

If a null hypothesis was not rejected at the 0.10 level of significance, it will be rejected at a 0.05 level of significance based on the same sample results.

Answer 1

False

Question 2

The probability of committing a Type I error is called the power of the test.

Answer 2

False

Question 3

The rejection region for a hypothesis test becomes smaller if the level of significance is changed from 0.01 to 0.05.

Answer 3

False

Question 4

Whenever hypotheses are established such that the alternative hypothesis is "μ ≠ 8", where μ is the population mean, the hypothesis test would be a two-tailed test.

Question 5

The first step in testing a hypothesis is to establish a true null hypothesis and a false alternative hypothesis.

Question 6

Hypotheses are tentative explanations of a principle operating in nature.

Question 7

When a true null hypothesis is rejected, the researcher has made a Type I error.

Question 8

If a null hypothesis was rejected at the 0.025 level of significance, it will be rejected at a 0.01 level of significance based on the same sample results.

Question 9

The probability of type II error becomes bigger if the level of significance is changed from 0.01 to 0.05.

Question 10

When a researcher fails to reject a false null hypothesis, a Type II error has been committed.

Question 11

In many cases a business researcher gathers data to test a hypothesis about a single population mean and the value of the population standard deviation is unknown.In this case the researcher cannot use the z test.

Question 12

Generally speaking, the hypotheses that business researchers want to prove are stated in the alternative hypothesis.

Question 13

In testing hypotheses, the researcher initially assumes that the alternative hypothesis is true and uses the sample data to reject it.

Question 14

Whenever hypotheses are established such that the alternative hypothesis is "μ>8", where μ is the population mean, the hypothesis test would be a two-tailed test.

Question 15

When a false null hypothesis is rejected, the researcher has made a Type II error.

Question 16

The null and the alternative hypotheses must be mutually exclusive and collectively exhaustive.

Question 17

Power is equal to (1 - $\beta$ ), the probability of a test rejecting the null hypothesis that is indeed false.

Question 18

If a null hypothesis is not rejected at the 0.05 level of significance, the p-value is bigger than 0.05

Question 19

Whenever hypotheses are established such that the alternative hypothesis is "μ > 8", where μ is the population mean, the p-value is the probability of observing a sample mean greater than the observed sample mean assuming that μ = 8.

Question 20

The rejection and nonrejection regions are divided by a point called the critical value.

Question 21

A z test of proportions is used when a hypothesis test is conducted on a population proportion.

Question 22

When the population standard deviation ( $\sigma$ )is unknown, the value of s - 1 is used to compute the t value.

Question 23

When using the t test to test a hypothesis about a population mean with an unknown population standard deviation ( $\sigma$ )the degrees of freedom is defined as n - 1.

Question 24

A "scientific hypothesis" _______________.

A)is a synonym for the term "scientific theory."
B)is disproven if a counterexample is found.
C)is a tentative explanation of some natural phenomena.
D)is a proven explanation of some natural phenomena.
E)may or may not be testable.

Question 25

Suppose that H_o: $\mu$$\le$ 0.01
H_a: $\mu$ > 0.01
The value 0.01 is the maximum safe level of some naturally occurring lethal pollutant in drinking water for human consumption.You need to decide if you will use water coming from a specific source for one of the beverages your company produces, based on sample measures of this pollutant taken in random different locations and times at the source of water.In this case you would want to

A)maximize the power of the test.
B)maximize β.
C)minimize $\mu$ .
D)maximize the significance, α.
E)maximize 1 - α.

Question 26

A statistically significant result is _______________.

A)a result that is likely due to chance.
B)a result that is unlikely due to chance.
C)the same as a substantive result.
D)a result that is important for decision makers.
E)a result that leads to the rejection of the alternative hypothesis.

Question 27

The value of committing a Type II error is defined by the researcher prior to the study.

Question 28

Increasing the sample size reduces the probability of committing a Type I and Type II simultaneously.

Question 29

If the p-value for a one-tailed test is 0.019, then the null hypothesis

A)can be rejected at a significance level of 0.01.
B)would be rejected or not rejected depending on the value of the statistic (the observed value).
C)would be rejected or not rejected depending on the value of the statistic and the critical value.
D)can be rejected at a significance level of 0.10.
E)may or may not be rejected, but there is no enough information to answer this question.

Question 30

The probability of committing a Type II error changes for each alternative value of the parameter.

Question 31

In testing a hypothesis about a population mean with an unknown population standard deviation ( $\sigma$ )the degrees of freedom is used in the denominator of the test statistic.

Question 32

If the observed chi-squared value is more than the critical chi-squared value found on the related table, then the null hypothesis is rejected.

Question 33

A business is testing a new product that in reality would make the company money.Based on market research data, the business analyst committed a Type II error by rejecting the null.

Question 34

If car manufacturer of cars orders the windshields from another company.The width of the windshields received need to be within 0.2 mm of the average width.The contract between the car manufacturer and the windshield suppler should include a clause related to the delivered windshields' median.

Question 35

Business researchers sometimes need to test for equality of population variance.The hypothesis test about a population variance is performed using a chi-square test.

Question 36

The p-value is

A)the probability that the alternative hypothesis is true.
B)the probability that the null hypothesis is true.
C)the probability of a statistic being at most as extreme as the observed value when H_o is true.
D)the probability of a statistic being at most as extreme as the observed value when H_o is false.
E)the probability of a statistic being at least as extreme as the observed value when H_o is true.

Question 37

When conducting a hypothesis test on a population proportion, the value of q is defined as p + 1.

Question 38

In conducting the z test of proportions, the sample proportion is computed by dividing the number of items being counted by the estimated total population.

Question 39

If the null hypothesis is in reality false, but the sample data leads the analyst to fail to reject the null, then the analysts has made a Type II error.

Question 40

In testing a hypothesis about a population variance, the chi-square test is fairly robust to the assumption the population is normally distributed.

Question 41

In a two-tailed hypothesis about a population mean with a sample size of 100, $\sigma$ is known, and α = 0.05, the rejection region would be _______.

A)z > 1.64
B)z > 1.96
C)z < -1.96 and z > 1.96
D)z < -1.64 and z > 1.64
E)z < -2.33 and z > 2.33

Question 42

Suppose you are testing the null hypothesis that a population mean is less than or equal to 46, against the alternative hypothesis that the population mean is greater than 46.The sample size is 25 and α =.05.If the sample mean is 50 and the population standard deviation is 8, the observed z value is _______.

A)2.5
B)-2.5
C)6.25
D)-6.25
E)12.5

Question 43

Consider the following null and alternative hypotheses. H_o: $\mu$ $\le$ 67
H_a: $\mu$ > 67
These hypotheses _______________.

A)indicate a one-tailed test with a rejection area in the right tail
B)indicate a one-tailed test with a rejection area in the left tail
C)indicate a two-tailed test
D)are established incorrectly
E)are not mutually exclusive

Question 44

A home building company routinely orders standard interior doors with a height of 80 inches.Recently the installers have complained that the doors are not the standard height.The quality control inspector for the home building company is concerned that the manufacturer is supplying doors that are not 80 inches in height.In an effort to test this, the inspector is going to gather a sample of the recently received doors and measure the height.The alternative hypothesis for the statistical test to determine if the doors are not 80 inches is __________.

A)the mean height is > 80 inches
B)the mean height is < 80 inches
C)the mean height is = 80 inches
D)the mean height is ≠ 80 inches
E)the mean height is ≥ 80 inches

Question 45

A researcher is testing a hypothesis of a single mean.The critical z value for $\alpha$ = .05 in a one-tailed test is 1.645.The observed z value from sample data is 1.13.The decision made by the researcher based on this information is to ______ the null hypothesis.

A)reject
B)fail to reject
C)redefine
D)change the alternate hypothesis
E)restate

Question 46

A researcher is testing a hypothesis of a single mean.The critical z value for $\alpha$ = .05 in a two-tailed test is +1.96.The observed z value from sample data is -2.11.The decision made by the researcher based on this information is to _____ the null hypothesis.

A)reject
B)fail to reject
C)redefine
D)change the alternate hypothesis
E)restate

Question 47

A coffee-dispensing machine is supposed to deliver 8 ounces of liquid into each paper cup, but a consumer believes that the actual mean amount is less.The consumer obtained a sample of 49 cups of the dispensed liquid with average of 7.75 ounces.If the sample variance of the dispensed liquid per cup is 0.81 ounces, and α = 0.05, the p-value is approximately __________.

A)0.05
B)0.025
C)0.06
D)0.015
E)0.10

Question 48

Suppose you are testing the null hypothesis that a population mean is greater than or equal to 60, against the alternative hypothesis that the population mean is less than 60.The sample size is 64 and $\alpha$ = .05.If the sample mean is 58 and the population standard deviation is 16, the observed z value is _______.

A)-1
B)1
C)-8
D)8
E)58

Question 49

Consider the following null and alternative hypotheses. H_o: $\mu$ $\ge$ 67
H_a: $\mu$ < 67
These hypotheses _______________.

A)indicate a one-tailed test with a rejection area in the right tail
B)indicate a one-tailed test with a rejection area in the left tail
C)indicate a two-tailed test
D)are established incorrectly
E)are not mutually exclusive

Question 50

Consider the following null and alternative hypotheses. H_o: $\mu$ = 67
H_a: $\mu$ $\neq$ 67
These hypotheses ______________.

A)indicate a one-tailed test with a rejection area in the right tail
B)indicate a one-tailed test with a rejection area in the left tail
C)indicate a two-tailed test
D)are established incorrectly
E)are not mutually exclusive

Question 51

A coffee-dispensing machine is supposed to deliver 8 ounces of liquid into each paper cup, but a consumer believes that the actual mean amount is less.The consumer obtained a sample of 49 cups of the dispensed liquid with average of 7.75 ounces.If the sample variance of the dispensed liquid delivered per cup is 0.81 ounces, and α = 0.05, the appropriate decision is to ________.

A)increase the sample size
B)reduce the sample size
C)fail to reject the 8-ounces claim
D)maintain status quo
E)reject the 8-ounces claim

Question 52

Suppose you are testing the null hypothesis that a population mean is less than or equal to 46, against the alternative hypothesis that the population mean is greater than 46.If the sample size is 25, $\sigma$ is known, and α = .01, the critical value of z is _______.

A)1.645
B)-1.645
C)1.28
D)-2.33
E)2.33

Question 53

The local swim team is considering offering a new semi-private class aimed at entry-level swimmers, but needs a minimum number of swimmers to sign up in order to be cost effective.Last year's data showed that during 8 swim sessions the average number of entry-level swimmers attending was 15.Suppose the instructor wants to conduct a hypothesis test and the alternative hypothesis is "the population mean is greater than 15." If the sample size is 5, $\sigma$ is known, and α = .01, the critical value of z is _______.

A)2.575
B)-2.575
C)2.33
D)-2.33
E)2.45

Question 54

In a two-tailed hypothesis about a population mean with a sample size of 100, $\sigma$ is known, and α = 0.10, the rejection region would be _______.

A)z > 1.64
B)z > 1.28
C)z < -1.28 and z > 1.28
D)z < -1.64 and z > 1.64
E)z < -2.33 and z > 2.33

Question 55

The customer help center in your company receives calls from customers who need help with some of the customized software solutions your company provides.Your company claims that the average waiting time is 7 minutes at the busiest time, from 8 a.m.to 10 a.m., Monday through Thursday.One of your main clients has recently complained that every time she calls during the busy hours, the waiting time exceeds 7 minutes.You conduct a statistical study to determine the average waiting time with a sample of 35 calls for which you obtain an average waiting time of 8.15 minutes.If the population standard deviation is known to be 4.2 minutes, and α = 0.05, the appropriate decision is to ___________.

A)increase the sample size
B)reduce the sample size
C)fail to reject the 7-minute average waiting time claim
D)maintain status quo
E)reject the 7-minute claim

Question 56

A researcher is testing a hypothesis of a single mean.The critical z value for $\alpha$ = .05 in a two-tailed test is +1.96.The observed z value from sample data is 2.85.The decision made by the researcher based on this information is to _____ the null hypothesis.

A)reject
B)fail to reject
C)redefine
D)change the alternate hypothesis
E)restate

Question 57

Jennifer Cantu, VP of Customer Services at Tri-State Auto Insurance, Inc., monitors the claims processing time of the claims division.Her standard includes "a mean processing time of 5 days or less." Each week, her staff checks for compliance by analyzing a random sample of 60 claims.Jennifer's null hypothesis is ________.

A) $\mu$ > 5
B) $\mu$ > 5
C)n = 60
D) $\mu$ < 5
E) $\mu$ = =5 On page 273 of the text, it states that the null hypothesis is always just =, even in one taled tests.

Question 58

The local swim team is considering offering a new semi-private class aimed at entry-level swimmers, but needs at minimum number of swimmers to sign up in order to be cost effective.Last year's data showed that during 8 swim sessions the average number of entry-level swimmers attending was 15.Suppose the instructor wants to conduct a hypothesis test.The alternative hypothesis for this hypothesis test is: "the population mean is less than 15".The sample size is 8, $\sigma$ is known, and α =.05, the critical value of z is _______.

A)1.645
B)-1.645
C)1.96
D)-1.96
E)2.05

Question 59

The customer help center in your company receives calls from customers who need help with some of the customized software solutions your company provides.Your company claims that the average waiting time is 7 minutes at the busiest time, from 8 a.m.to 10 a.m., Monday through Thursday.One of your main clients has recently complained that every time she calls during the busy hours, the waiting time exceeds 7 minutes.You conduct a statistical study to determine the average waiting time with a sample of 35 calls for which you obtain an average waiting time of 8.15 minutes.If the population standard deviation is known to be 4.2 minutes, and α = 0.05, the p-value is approximately

A)0.025
B)0.026
C)0.05
D)0.053
E)0.10

Question 60

A researcher is testing a hypothesis of a single mean.The critical z value for $\alpha$ = .05 in a two-tailed test is +1.96.The observed z value from sample data is -1.85.The decision made by the researcher based on this information is to _____ the null hypothesis.

A)reject
B)fail to reject
C)redefine
D)change the alternate hypothesis
E)restate

Question 61

A political scientist wants to prove that a candidate is currently carrying more than 60% of the vote in the state.She has her assistants randomly sample 200 eligible voters in the state by telephone and only 90 declare that they support her candidate.The observed z value for this problem is _______.

A)-4.33
B)4.33
C)0.45
D)-.31
E)2.33

Question 62

In performing a hypothesis test where the null hypothesis is that the population mean is 4.8 against the alternative hypothesis that the population mean is not equal to 4.8, a random sample of 25 items is selected.The sample mean is 4.1 and the sample standard deviation is 1.4.It can be assumed that the population is normally distributed.The observed "t" value for this problem is _______.

A)-12.5
B)12.5
C)-2.5
D)-0.7
E)0.7

Question 63

In performing a hypothesis test where the null hypothesis is that the population mean is 4.8 against the alternative hypothesis that the population mean is not equal to 4.8, a random sample of 25 items is selected.The sample mean is 4.1 and the sample standard deviation is 1.4.It can be assumed that the population is normally distributed.The degrees of freedom associated with this are _______.

A)25
B)24
C)26
D)2
E)1

Question 64

A company believes that it controls more than 30% of the total market share for one of its products.To prove this belief, a random sample of 144 purchases of this product is contacted.It is found that 50 of the 144 purchases were of this company's brand.If a researcher wants to conduct a statistical test for this problem, the observed z value would be _______.

A)0.05
B)0.103
C)0.35
D)1.24
E)1.67

Question 65

The weight of a USB flash drive is 30 grams and is normally distributed.Periodically, quality control inspectors at Dallas Flash Drives randomly select a sample of 17 USB flash drives.If the mean weight of the USB flash drives is too heavy or too light the machinery is shut down for adjustment; otherwise, the production process continues.The last sample showed a mean and standard deviation of 31.9 and 1.8 grams, respectively.Using $\alpha$ = 0.10, the appropriate decision is to _______.

A)reject the null hypothesis and shut down the process
B)reject the null hypothesis and do not shut down the process
C)fail to reject the null hypothesis and shut down the process
D)fail to reject the null hypothesis and do not shut down the process)do nothing

Question 66

The local oil changing business is very busy on Saturday mornings and is considering expanding.A national study of similar businesses reported the mean number of customers waiting to have their oil changed on Saturday morning is 3.6.Suppose the local oil changing business owner, wants to perform a hypothesis test.The null hypothesis is the population mean is 3.6 and the alternative hypothesis is the population mean is not equal to 3.6.The owner takes a random sample of 16 Saturday mornings during the past year and determines the sample mean is 4.2 and the sample standard deviation is 1.4.It can be assumed that the population is normally distributed.The level of significance is 0.05.The decision rule for this problem is to reject the null hypothesis if the observed "t" value is _______.

A)less than -2.131 or greater than 2.131
B)less than -1.761 or greater than 1.761
C)less than -1.753 or greater than 1.753
D)less than -2.120 or greater than 2.120
E)less than -3.120 or greater than 3.120

Question 67

The customer help center in your company receives calls from customers who need help with some of the customized software solutions your company provides.Your company claims that the average waiting time is 7 minutes at the busiest time, from 8 a.m.to 10 a.m., Monday through Thursday.One of your main clients has recently complained that every time she calls during the busy hours, the waiting time exceeds 7 minutes.You conduct a statistical study to determine the average waiting time with a sample of 35 calls, for which you obtain an average waiting time of 8.15 minutes.Suppose that you can assume that waiting times are normally distributed.The sample standard deviation is 4.2 minutes.The null hypothesis is:

A)n $\neq$ 35
B)n = 35
C) $\mu$ = 7
D) $\mu$ $\neq$ 7
E) $\mu$ > 7

Question 68

A company believes that it controls more than 30% of the total market share for one of its products.To prove this belief, a random sample of 144 purchases of this product is contacted.It is found that 50 of the 144 purchases were of this company's brand.If a researcher wants to conduct a statistical test for this problem, the test would be _______.

A)a one-tailed test
B)a two-tailed test
C)an alpha test
D)a finite population test
E)a finite sample test

Question 69

A small restaurant owner believes no more than 36% of his customers travel over 10 miles to his business.He is interested in expanding his customer base through marketing.However, he would like to test his hypothesis prior to investing money in a marketing initiative.He intends to use the following null and alternative hypotheses. H_o: p $\le$ 0.36
H_a: p > 0.36
These hypotheses _______________.

A)indicate a one-tailed test with a rejection area in the right tail
B)indicate a one-tailed test with a rejection area in the left tail
C)indicate a two-tailed test
D)are established incorrectly
E)are not mutually exclusive

Question 70

Suppose a researcher is testing a null hypothesis that $\mu$ = 61.A random sample of n = 36 is taken resulting in a sample mean of 63 and s = 9.The observed test statistic is _______.

A)-0.22
B)0.22
C)1.33
D)8.08
E)7.58

Question 71

The weight of a USB flash drive is 30 grams and is normally distributed.Periodically, quality control inspectors at Dallas Flash Drives randomly select a sample of 17 USB flash drives.If the mean weight of the USB flash drives is too heavy or too light the machinery is shut down for adjustment; otherwise, the production process continues.The last sample showed a mean and standard deviation of 31.9 and 1.8 grams, respectively.Using $\alpha$ = 0.10, the critical "t" values are _______.

A)-2.120 and 2.120
B)-2.131 and 2.131
C)-1.753 and 1.753
D)-1.746 and 1.746
E)-2.567 and 2.567

Question 72

The local oil changing business is very busy on Saturday mornings and is considering expanding.A national study of similar businesses reported the mean number of customers waiting to have their oil changed on Saturday morning is 3.6.Suppose the local oil changing business owner, wants to perform a hypothesis test.The null hypothesis is the population mean is 3.6 and the alternative hypothesis that the population mean is not equal to 3.6.The owner takes a random sample of 16 Saturday mornings during the past year and determines the sample mean is 4.2 and the sample standard deviation is 1.4.It can be assumed that the population is normally distributed and the level of significance is 0.05.The critical value found in the "t" table for this problem is _______.

A)1.753
B)2.947
C)2.120
D)2.131
E)2.311

Question 73

In performing a hypothesis test where the null hypothesis is that the population mean is 23 against the alternative hypothesis that the population mean is not equal to 23, a random sample of 17 items is selected.The sample mean is 24.6 and the sample standard deviation is 3.3.It can be assumed that the population is normally distributed.The degrees of freedom associated with this are _______.

A)17
B)16
C)15
D)2
E)1

Question 74

The weight of a USB flash drive is 30 grams and is normally distributed.Periodically, quality control inspectors at Dallas Flash Drives randomly select a sample of 17 USB flash drives.If the mean weight of the USB flash drives is too heavy or too light the machinery is shut down for adjustment; otherwise, the production process continues.The last sample showed a mean and standard deviation of 31.9 and 1.8 grams, respectively.The null hypothesis is ______.

A)n $\neq$ 17
B)n = 17
C) $\mu$ = 30
D) $\mu$ $\neq$ 30
E) $\mu$ ≥ 34.9

Question 75

A small restaurant owner believes at least 36 % of his customers would be willing to order take out service if it were available.He is interested in surveying his customer base.He intends to use the following null and alternative hypotheses. H_o: p $\ge$ 0.36
H_a: p < 0.36
These hypotheses _______________.

A)indicate a one-tailed test with a rejection area in the right tail
B)indicate a one-tailed test with a rejection area in the left tail
C)indicate a two-tailed test
D)are established incorrectly
E)are not mutually exclusive

Question 76

The customer help center in your company receives calls from customers who need help with some of the customized software solutions your company provides.Previous studies had indicated that 20% of customers who call the help center are Hispanics whose native language is Spanish and therefore would prefer to talk to a Spanish-speaking representative.This figure coincides with the national proportion, as shown by multiple larger polls.You want to test the hypothesis that 20% of the callers would prefer to talk to a Spanish-speaking representative.You conduct a statistical study with a sample of 35 calls and find out that 11 of the callers would prefer a Spanish-speaking representative.The significance level for this test is 0.01.The value of the test statistic obtained is:

A)0.008
B)0.29
C)0.58
D)1.69
E)1.73

Question 77

A company believes that it controls more than 30% of the total market share for one of its products.To prove this belief, a random sample of 144 purchases of this product is contacted.It is found that 50 of the 144 purchases were of this company's brand.If a researcher wants to conduct a statistical test for this problem, the alternative hypothesis would be _______.

A)the population proportion is less than 0.30
B)the population proportion is greater than 0.30
C)the population proportion is not equal to 0.30
D)the population mean is less than 40
E)the population mean is greater than 40

Question 78

In performing hypothesis tests about the population mean, if the population standard deviation is not known, a t test can be used to test the mean if _________________.

A)n is small
B)the sample is random
C)the population mean is known
D)the population is normally distributed
E)the population is chi-square distributed

Question 79

The local oil changing business is very busy on Saturday mornings and is considering expanding.A national study of similar businesses reported the mean number of customers waiting to have their oil changed on Saturday morning is 3.6.Suppose the local oil changing business owner, wants to perform a hypothesis test.The null hypothesis is the population mean is 3.6 and the alternative hypothesis that the population mean is not equal to 3.6.The owner takes a random sample of 16 Saturday mornings during the past year and determines the sample mean is 4.2 and the sample standard deviation is 1.4.It can be assumed that the population is normally distributed.The observed "t" value for this problem is _______.

A)0.05
B)0.43
C)1.71
D)1.33
E)0.71

Question 80

A coffee-dispensing machine is supposed to deliver 8 ounces of liquid into each paper cup, but a consumer believes that the actual mean amount is less.The consumer obtained a sample of 16 cups of the dispensed liquid with sample mean of 7.75 ounces and sample variance of 0.81 ounces.If the dispensed liquid delivered per cup is normally distributed, the appropriate decision at α = 0.05 is to ___________.

A)increase the sample size
B)reduce the sample size
C)fail to reject the 8-ounces claim
D)maintain status quo
E)reject the 8-ounces claim